I feel quite a bit of sympathy for Oedipus in this story, despite his hard-headed pride.
His character offers plenty to dislike (unwillingness to see the obvious, a tendency to interupt at the worst moment, a quickness to anger, a refusal to take advice), but he is noble. Oedipus marries his mother, yes, but only because he is trying not to. He kills his father, yes, but only because he is fleeing from the possibility of killing his father.
He is caught in a fate that he cannot escape. It's hard to look at him without some sympathy.
"Abhor" may be too strong a word, but it is certainly possible to have highly mixed emotions (and thoughts) about Oedipus, because he is an extremely complex character who finds himself in an immensely complicated situation. Both of these factors almost demand, in return, complex and complicated reactions from the play's audience. One reason that the play is so justly celebrated is precisely because both it and its central figure are highly complex.
This is an excellent question. The answer is: of course! The reason for this is rooted in the nature of Greek tragedy or more precisely in the nature of the tragic hero.
The fact that Oedipus is both tragic and heroic makes him loved and abhorred. The tragic element of Oedipus's life is that he killed his father, married his mother, and lacked self-knowledge. On the other hand, Oedipus is heroic. He loves his people, the citizens of Thebes. He would do anything to save them. From this perspective, he was a great leader. Second, Oedipus is intelligent. For example, he solved the riddle of the Sphinx. Finally, he is decisive and courageous. In light of these point, Oedipus is truly heroic. Apart from his flaws, he is an ideal leader.
All tragic heroes have two sides to them.